Abstract
AbstractFor p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large gaps between tu1 and tu2.
Publisher
Cambridge University Press (CUP)
Reference9 articles.
1. 4. Peter, F. , Miller, A. N. and Pinzon-Caicedo, J. . A note on the topological slice genus of satellite knots. arXiv:1908.03760 (2019).
2. The unknotting number and classical invariants, I
3. 8. McCoy, D. . Null-homologous twisting and the algebraic genus. arXiv:1908.4043 (2019).
4. 1. Baader, S. , Banfield, I. and Lewark, L. , Untwisting 3-strand torus knots. arXiv:1909.01003 (2019).
5. On the algebraic unknotting number
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Unknotting via null-homologous twists and multitwists;Pacific Journal of Mathematics;2024-07-22
2. Slicing knots in definite 4-manifolds;Transactions of the American Mathematical Society;2024-06-11
3. Untwisting 3‐strand torus knots;Bulletin of the London Mathematical Society;2020-04-22